The paper studies the spatial motion of a rigid body in a resisting medium under the action of a follower force that causes the center of mass to move rectilinearly and uniformly. The body, which is axisymmetric and homogeneous, interacts with the medium by its frontal area that has the form of a flat circular disk. Since there is no exact analytic description of the forces and torques exerted by the medium on the disk, the problem is “immersed” in a wider class of problems. Partial solutions and phase portraits in the three-dimensional space of quasivelocities are obtained for the dynamic systems under consideration. The transcendental first integrals of the dynamic part of the equations of motion are listed
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References
G. S. Byushgens and R. V. Studnev, Dynamics of Longitudinal and Lateral Motion [in Russian], Mashinostoenie, Moscow (1969).
G. S. Byushgens and R. V. Studnev, Aircraft Dynamics. Spatial Motion [in Russian], Mashinostroenie, Moscow (1988).
M. I. Gurevich, The Theory of Jets in an Ideal Fluid, Nauka, Moscow (1979).
V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, “Motion of a body in a separated flow of a resisting medium: A model problem,” Izv. RAN, Mekh. Zhid. Gaza, No. 3, 23–27 (1995).
H. L. Lamb, Hydrodynamics, Cambridge Univ. Press, Cambridge (1932).
B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov, An Introduction to the Motion of a Body in a Resisting Medium [in Russian], Izd. MGU, Moscow (1986).
V. A. Samsonov, M. V. Shamolin, V. A. Eroshin, and V. M. Makarshin, “Mathematical simulation of the motion of a body in a separated flow of a resisting medium,” Report No. 4396, Inst. Mekh. MGU, Moscow (1995).
S. A. Chaplygin, Selected Works [in Russian], Nauka, Moscow (1976).
S. A. Chaplygin, “On motion of heavy bodies through an incompressible fluid,” in: Complete Works [in Russian], Vol. 1, Izd. AN SSSR, Leningrad (1933), pp. 133–135.
M. V. Shamolin, “An introduction to the motion of a body in a resisting medium. A new two-parameter set of phase portraits,” Vestn. MGU, Ser. 1, Mat. Mekh., No. 4, 57–69 (1996).
M. V. Shamolin, “Closed trajectories of different topological types in the problem of motion of a body through a resisting medium,” Vestn. MGU, Ser. 1, Mat. Mekh., No. 2, 52–56 (1992).
M. V. Shamolin, Methods for the Analysis of Dynamic Systems with Variable Dissipation in Rigid-Body Dynamics [in Russian], Ekzamen, Moscow (2007).
M. V. Shamolin, “Variety of types of phase portraits in the dynamics of a rigid body interacting with a resisting medium,” Dokl. RAN, 349, No. 2, 193–197 (1996).
M. V. Shamolin, “Some classes of partial solutions in the dynamics of a rigid body interacting with a medium,” Izv. RAN, Mekh. Tverd. Tela, No. 2, 178–189 (1999).
M. V. Shamolin, “Spatial topographical systems of Poincare and comparison systems,” Russ. Math. Surv., 52, No. 3, 621–622 (1997).
V. D. Kubenko and T. A. Marchenko, “Nonstationary indentation of a rigid blunt indenter into an elastic layer: A plane problem,” Int. Appl. Mech., 44, No. 3, 286–295 (2008).
V. D. Kubenko and T. A. Marchenko, “Nonstationary indentation of a blunt rigid body into an elastic layer: An axisymmetric problem,” Int. Appl. Mech., 44, No. 7, 747–756 (2008).
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Translated from Prikladnaya Mekhanika, Vol. 46, No. 7, pp. 120–133, July 2010
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Shamolin, M.V. Spatial motion of a rigid body in a resisting medium. Int Appl Mech 46, 835–846 (2010). https://doi.org/10.1007/s10778-010-0373-6
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DOI: https://doi.org/10.1007/s10778-010-0373-6